Boudin argued and won unanimously the first case in which the United States Supreme Court invalidated a federal statute under the Free Speech Clause of the First Amendment, Lamont v. Postmaster General.[4] He also argued and won the landmark case Kennedy v. Mendoza-Martinez, in which the Supreme Court held that draft dodgers could not be stripped of their citizenship without being criminally prosecuted and afforded the protections promised to criminal defendants in the Fifth and Sixth Amendments.

He married Jean Roisman, a poet. Together they had two children, Michael and Kathy, who achieved recognition in later life.[7]Michael Boudin became a jurist and is currently a judge of the United States Court of Appeals for the First Circuit, serving as its chief judge 2001-2008. Kathy Boudin was an activist and co-founder of the 1960s radical group the Weather Underground, who served 22 years in prison for her role in a 1981 robbery that left two police officers and a security guard dead. His only biological grandson, Chesa Boudin, Kathy's son, is an attorney and writer.